## Topological quantum

Material type: TextPublisher: New York : Oxford University Press, [c2023]Description: 611 pISBN: 9780198886723LOC classification: QC23.2.S56Item type | Current library | Collection | Shelving location | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|---|

Book | ICTS | Physics | Rack No 9 | QC23.2.S56 (Browse shelf (Opens below)) | Checked out | 07/22/2024 | 02830 |

1.:Introduction and Ancient History

2.:Kauffman Bracket Invariant and Relation to Physics

I Anyons and Topological Quantum Field Theories

3.:Particle Quantum Statistics

4.:Aharonov-Bohm Effect and Charge-Flux Composites

5.:Chern-Simons Theory Basics

6.:Short Digression on Quantum Gravity

7.:Defining Topological Quantum Field Theory

II Anyon Basics

8.:Fusion and Structure of Hilbert Space

9.:Change of Basis and F-Matrices

10.:Exchanging Identical Particles

11.:Computing with Anyons

III Anyon Diagrammatics

12.:Planar Diagrams

13.:Braiding Diagrams

14.:Seeking Isotopy

15.:Twists

16.:Nice Theories with Planar or Three-Dimensional Isotopy

17.:Further Structure

IV Some Examples: Planar Diagrams and Anyon Theories

18.:Some Simple Examples

19.:Anyons From Discrete Groups Elements

20.:Bosons and Fermions from Group Representati

21.:Quantum Groups (In Brief)

22.:Temperly-Lieb Algebra and Jones-Kauffman Anyons

V Applications of TQFT Diagrammatics

23.:State Sum TQFTs

24.:Formal Construction of “Chern-Simons” TQFT: Surgery and More Complicated Manifolds

25.:Anyon Condensation

VI Toric Code Basics

26.:Introducing Quantum Error Correction

27.:Introducing the Toric Code

28.:The Toric Code as a Phase of Matter and a TQFT

29.:Robustness of Topologically-Ordered Matter

30.:Abstracting the Toric Code: Introduction to Tube Algebra

VII More General Loop-Gas and String-Net Models

31.:Kitaev Quantum Double Model

32.:Doubled-Semion Model

33.:Levin-Wen String-Net

VIII Entanglement and Symmetries

34.:Topological Entanglement

35.:SPT Phases of Matter

36.:Anyon Permuting Symmetry

IX Further Thoughts

37.:37 Experiments (In Brief)

38.:Final Comments

39.:Appendix: Kac and Other Resources for TQFTs

40.:Appendix: Some Mathematical Basics

At the intersection of physics, mathematics, and computer science, an exciting new field of study has formed, known as “Topological Quantum.” This research field examines the deep connections between the theory of knots, special types of subatomic particles known as anyons, certain phases of matter, and quantum computation. This book elucidates this nexus, drawing in topics ranging from quantum gravity to topology to experimental condensed matter physics. Topological quantum has increasingly been a focus point in the fields of condensed matter physics and quantum information over the last few decades, and the forefront of research now builds on the basic ideas presented in this book. The material is presented in a down-to-earth and entertaining way that is far less abstract than most of what is in the literature. While introducing the crucial concepts and placing them in context, the subject is presented without resort to the highly mathematical category theory that underlies the field.

Requiring only an elementary background in quantum mechanics, this book is appropriate for all readers, from advanced undergraduates to the professional practitioner. This book will be of interest to mathematicians and computer scientists as well as physicists working on a wide range of topics. Those interested in working in these field will find this book to be an invaluable introduction as well as a crucial reference.--- summary provided by the publisher

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